Scuba divers know that the deeper they dive, the more light is absorbed by the water above them. On a dive, Petra's light meter shows that the amount of light available decreases by 10% for every 10 m that she descends.

a) Write the exponential function that relates the amount, L, as a percent expressed as a decimal, of light available to the depth, d, in 10-m increments.

b) What are the domain and range of the function for this situation?

c) What percent of light will reach Petra if she dives to a depth of 25 m?

A

f (x) = L*0.90) ^ (x/10) where x is the depth in meters.

B

The domain is x>=0, The range is y = < L

C

f (25) = L*0.90^ (25/10)

f (25) = 0.768 L or 76.8% of what the intensity was on the surface.

Someone wants me to correct the formula. I dispute the answer key. The answer cannot be d without taking into account that L decreases every 10 meters. d does not take into account the 10 meters. Without that, the answer is quite different and far too small.

As to the domain and range, the comments below the answer take care of that. If you know how to use the more formal notation use that. I accepted it for the person answering the question.